@teorth.bsky.social wrote a clear, nontechnical explanation of the Kakeya Conjecture (for which Hong Wang won the Fields Medal in July), why it matters, how it was solved, and future directions, and posted it on the arXiv: arxiv.org/abs/2608.22209
arxiv.orgRotating needles in space: the road to the Kakeya conjecture, and why it mattersA non-technical exposition of the Kakeya conjecture, why it matters, and the road to the solution of this conjecture in three dimensions by Hong Wang and Joshua Zahl.